Showing papers in "American Journal of Physics in 2005"
TL;DR: The prisoner’s dilemma is employed to discuss new insights gained in behavioral ecology using methods from physics to reveal critical phase transitions that fall into the universality class of directed percolation on square lattices and mean-field-type transitions on regular small world networks and random regular graphs.
Abstract: Evolutionary game theory is designed to capture the essentials of the characteristic interactions among individuals. Its most prominent application is the quest for the origins and evolution of cooperation. The effects of population structures on the performance of behavioral strategies became apparent only in recent years and marks the advent of an intriguing link between apparently unrelated disciplines. Evolutionary game theory in structured populations reveals critical phase transitions that fall into the universality class of directed percolation on square lattices and mean-field-type transitions on regular small world networks and random regular graphs. We employ the prisoner’s dilemma to discuss new insights gained in behavioral ecology using methods from physics.
448 citations
TL;DR: In this paper, the authors highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that often is assumed to be the dominant effect.
Abstract: Objects that float at the interface between a liquid and a gas interact because of interfacial deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that often is assumed to be the dominant effect. We emphasize this point using a simple classroom demonstration, and then derive the physical conditions leading to mutual attraction or repulsion. We also quantify the force of interaction in particular instances and present a simple dynamical model of this interaction. The results obtained from this model are validated by comparison to experimental results for the mutual attraction of two identical spherical particles. We consider some of the applications of the effect that can be found in nature and the laboratory.
428 citations
TL;DR: Gerry et al. as discussed by the authors reviewed Introductory Quantum Optics by Christopher C. Gerry, Peter L. Knight, and Peter A. Knight. 317 pp., New York, 2005. Price: $55.00
Abstract: This article reviews Introductory Quantum Optics by Christopher C. Gerry, Peter L. Knight . 317 pp. , New York, 2005. Price: $55.00 (paper) ISBN 0-521-52735-X.
380 citations
Abstract: We examined normalized gains and preinstruction scores on the force concept inventory (FCI) for students in interactive engagement courses in introductory mechanics at four universities and found a significant, positive correlation for three of them. We also examined class average FCI scores of 2948 students in 38 interactive engagement classes, 31 of which were from the same four universities and 7 of which came from 3 other schools. We found a significant, positive correlation between class average normalized FCI gains and class average preinstruction scores. To probe this correlation, we administered Lawson’s classroom test of scientific reasoning to 65 students and found a significant, positive correlation between these students’ normalized FCI gains and their Lawson test scores. This correlation is even stronger than the correlation between FCI gains and preinstruction FCI scores. Our study demonstrates that differences in student populations are important when comparing normalized gains in different interactive engagement classes. We suggest using the Lawson test along with the FCI to measure the effectiveness of alternative interactive engagement strategies.
261 citations
TL;DR: In this paper, a case study of the influence of epistemology on learning for a student in an introductory college physics course is presented, showing that a student's personal epistemological stance can have a direct, causal influence on her learning of physics.
Abstract: We discuss a case study of the influence of epistemology on learning for a student in an introductory college physics course. An analysis of videotaped class work, written work, and interviews indicates that many of the student’s difficulties were epistemological in nature. Our primary goals are to show instructors and curriculum developers that a student’s personal epistemological stance—her ideas about knowledge and learning—can have a direct, causal influence on her learning of physics, and to describe a mechanism for this interaction. This influence exists even when research-based curriculum materials provide implicit epistemological support. For this reason, curriculum materials and teaching techniques could become more effective by explicitly attending to students’ epistemologies.
253 citations
TL;DR: In this paper, an analysis of data on students' problem-solving performance on similar Newton's third-law questions posed in diverse representations was presented. But the results showed that females had higher error rates on circuit-diagram problems in comparison with males, although both males and females had received identical instruction.
Abstract: An analysis is presented of data on students’ problem-solving performance on similar problems posed in diverse representations. Five years of classroom data on 400 students collected in a second-semester algebra-based general physics course are presented. Two very similar Newton’s third-law questions, one posed in a verbal representation and one in a diagrammatic representation using vector diagrams, were given to students at the beginning of the course. The proportion of correct responses on the verbal question was consistently higher than on the diagrammatic question, and the pattern of incorrect responses on the two questions also differed consistently. Two additional four-question quizzes were given to students during the semester; each quiz had four very similar questions posed in the four representations: verbal, diagrammatic, mathematical/symbolic, and graphical. In general, the error rates for the four representations were very similar, but there was substantial evidence that females had a slightly higher error rate on the graphical questions relative to the other representations, whereas the evidence for male students was more ambiguous. There also was evidence that females had higher error rates on circuit-diagram problems in comparison with males, although both males and females had received identical instruction .
230 citations
TL;DR: In this article, the authors discuss the role of the speed of light in many physics equations and discuss the requirements for attaining consistency of the resulting equations, when what was previously a constant is made a dynamical variable.
Abstract: Theories for a varying speed of light have been proposed as an alternative way of solving several standard cosmological problems. Recent observational hints that the fine structure constant may have varied over cosmological scales have given impetus to these theories. However, the speed of light is hidden in many physics equations and plays different roles in them. We discuss these roles to shed light on proposals for varying speed of light theories. We also emphasize the requirements for attaining consistency of the resulting equations, when what was previously a constant is made a dynamical variable.
163 citations
TL;DR: This article found that many students cannot properly interpret or apply the ideal gas law after instruction in introductory physics and chemistry as well as more advanced courses, and identified some serious conceptual and reasoning difficulties that they have identified.
Abstract: Our findings from a long-term investigation indicate that many students cannot properly interpret or apply the ideal gas law after instruction in introductory physics and chemistry as well as more advanced courses. The emphasis in this paper is on the concepts of pressure, volume, and temperature at the macroscopic level. We describe some serious conceptual and reasoning difficulties that we have identified. Results from our research were applied in the design of a curriculum that has helped improve student understanding of the ideal gas law.
141 citations
TL;DR: In this article, the authors explain why the experiment fails for small dielectric thickness and discuss an improved version of the experiment using dielectrics sheets of various thicknesses rather than multiple thin sheets of a Dielectric.
Abstract: The availability of low cost digital multimeters capable of measuring capacitance has made parallel plate capacitor investigations common in the introductory laboratory. Typically, students add multiple thin sheets of dielectric material between conducting plates. The capacitance is measured and then plotted versus the reciprocal of the dielectric thickness (the nominal plate separation). We explain why the experiment fails for small dielectric thickness and discuss an improved version of the experiment using dielectric sheets of various thicknesses rather than multiple thin sheets of a dielectric.
134 citations
TL;DR: In this article, the authors describe five quantum mechanics experiments using correlated photons produced by parametric down conversion to generate interference patterns in interferometers, and analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman's rules, the state vector formalism, and amplitude packets.
Abstract: We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman’s rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2′×4′ optical breadboard.
123 citations
TL;DR: The Riemann Hypothesis has been studied for over 150 years as discussed by the authors, and the question of whether it is true or false has been the great white whale of mathematical research.
Abstract: In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark a " a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic a " defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark a " the Riemann Hypothesis a " that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows a " subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many a " the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof a " and those who have been consumed by it.
TL;DR: In this paper, the authors describe a long-term, large-scale investigation of the ability of university students to treat velocity and acceleration as vectors in one and two dimensions, finding that some serious conceptual and reasoning difficulties identified among introductory students also were common among pre-college teachers and physics graduate students.
Abstract: In this paper we describe a long-term, large-scale investigation of the ability of university students to treat velocity and acceleration as vectors in one and two dimensions. Some serious conceptual and reasoning difficulties identified among introductory students also were common among pre-college teachers and physics graduate students. Insights gained from this research guided the development of instructional materials that help improve student learning at the introductory level and beyond. The results have strong implications for the teaching of undergraduate physics, the professional development of teachers, and the preparation of teaching assistants.
TL;DR: In this article, student performance on conceptual understanding and on quantitative problem-solving ability in introductory mechanics in both studio and traditional classroom modes was evaluated. But, the performance of students in the studio sections performed the same or slightly worse on quantitative final exam problems.
Abstract: We present data on student performance on conceptual understanding and on quantitative problem-solving ability in introductory mechanics in both studio and traditional classroom modes. The conceptual measures used were the Force Concept Inventory and the Force and Motion Conceptual Evaluation. Quantitative problem-solving ability was measured with standard questions on the final exam. Our data compare three different quarters over the course of 2 years. In all three quarters, the normalized learning gain in conceptual understanding was significantly larger for students in the studio sections. At the same time, students in the studio sections performed the same or slightly worse on quantitative final exam problems.
TL;DR: In this article, a simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier, which has the advantage of yielding sensible results for energy eigenstates and does not require the use of time-dependent wave packets.
Abstract: A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model has the advantage of yielding sensible results for energy eigenstates and does not require the use of time-dependent wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not the absolute time of transit. A comparison is given with the weak-measurement post-selection calculations of Steinberg.
TL;DR: In this paper, the chiral Fierz-type completeness relations for SU(N) algebras were derived by using a chiral basis for the complex 4×4 matrices.
Abstract: General Fierz-type identities are examined and their well-known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex 4×4 matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning.
TL;DR: In this paper, the authors used voting machines with carefully designed sets of multiple-choice questions and instantaneous voting summaries to improve classroom dynamics and provided students with several opportunities per concept to test their understanding.
Abstract: A “voting machine” is a generic name for wireless-keypad in-class polling systems used by students to answer multiple-choice questions during lectures. We present our experiences gained while distributing and using voting machine modules. Using voting machines with carefully designed sets of multiple-choice questions and instantaneous voting summaries improved classroom dynamics and provided students with several opportunities per concept to test their understanding. Three question sets developed for the electricity and magnetism quarter of a year-long introductory physics course are included as examples.
TL;DR: Cheng as discussed by the authors reviewed Relativity, Gravitation and Cosmology: A Basic Introduction by Ta-Pei Cheng. 339 pp., New York, 2005. ISBN 0 19 852957.
Abstract: This article reviews Relativity, Gravitation and Cosmology: A Basic Introduction. by Ta-Pei Cheng . 339 pp. , New York, 2005. Price: $99.50 (cloth) ISBN 0-19-85295-6; $44.50 (paper) ISBN 0 19 852957.
TL;DR: The problems associated with the modification of Hamilton's principle to cover nonholonomic constraints by the application of the multiplier theorem of variational calculus are discussed in this article, and the reason for the problems is subtle and is discussed, together with the reason why the proper account of non-holonomic constraint is outside the scope of Hamilton’s variational principle.
Abstract: The problems associated with the modification of Hamilton’s principle to cover nonholonomic constraints by the application of the multiplier theorem of variational calculus are discussed. The reason for the problems is subtle and is discussed, together with the reason why the proper account of nonholonomic constraints is outside the scope of Hamilton’s variational principle. However, linear velocity constraints remain within the scope of D’Alembert’s principle. A careful and comprehensive analysis facilitates the resolution of the puzzling features of nonholonomic constraints.
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TL;DR: The origin of this division in terms of simple models of information gathering and utilizing systems (IGUSs) is discussed, where past, present, and future are not properties of four-dimensional spacetime but notions describing how individual IGUSs process information.
Abstract: The world is four-dimensional according to fundamental physics, governed by basic laws that operate in a spacetime that has no unique division into space and time. Yet our subjective experience is divided into present, past, and future. This paper discusses the origin of this division in terms of simple models of information gathering and utilizing systems (IGUSs). Past, present, and future are not properties of four-dimensional spacetime, but notions describing how individual IGUSs process information. Their origin is to be found in how these IGUSs evolved or were constructed. The past, present, and future of an IGUS is consistent with the four-dimensional laws of physics and can be described in four-dimensional terms. The present, for instance, is not a moment of time in the sense of a spacelike surface in spacetime. Rather, there is a localized notion of present at each point along an IGUS’ world line. The common present of many localized IGUSs is an approximate notion appropriate when they are sufficiently close to each other and have relative velocities much less than that of light. But modes of organization that are different from present, past, and future can be imagined that are consistent with the physical laws. We speculate why the present, past, and future organization might be favored by evolution and be therefore, a cognitive universal.
TL;DR: In this article, the authors argue for teaching the concepts of measurement and not only the calculations, and show that the fraction of students using range and not just average when comparing two data sets approximately doubled after instruction.
Abstract: For students to successfully complete an experiment, they must have an understanding of measurement and its related uncertainty. We argue for teaching the concepts of measurement and not only the calculations. An example of a concepts-based laboratory course is given, outlining the concepts presented, the design of the laboratory time, and the laboratory tasks. The concepts are briefly described and two often-overlooked concepts, predictive versus descriptive questions and internal versus external variation, are explained. Our survey results show that the fraction of students using range and not just average when comparing two data sets approximately doubled after instruction.
TL;DR: In this article, the authors present two simple analytical models that describe the dynamical process of gravitational collapse by which black holes and singularities form, which are analyzed in Eddington-Finkelstein and Painleve-Gullstrand coordinates.
Abstract: Most general relativity textbooks devote considerable attention to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. Only a few discuss the dynamical process of gravitational collapse by which black holes and singularities form. We present two simple analytical models that describe this process. The first involves collapsing spherical shells of light and is analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid and is analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is simplicity and algebraic completeness, but we also present a few more sophisticated results such as the collapse of a light shell in Kruskal-Szekeres coordinates.
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TL;DR: Einstein's Boxes as discussed by the authors is a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality, which was modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box.
Abstract: At the 1927 Solvay conference, Albert Einstein presented a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality. In the following years, the experiment was modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box. This paper collects together several formulations of this thought experiment from the literature, analyzes and assesses it from the point of view of the Einstein–Bohr debates, the EPR dilemma, and Bell’s theorem, and argues for “Einstein’s Boxes” taking its rightful place alongside similar but historically better known quantum mechanical thought experiments such as EPR and Schrodinger’s Cat.
TL;DR: This paper analyzed the effectiveness of working in pairs on the Conceptual Survey of Electricity and Magnetism test in a calculus-based introductory physics course and found that students who collaborated with a peer showed significantly larger normalized gain on individual testing than those who did not collaborate.
Abstract: We analyze the effectiveness of working in pairs on the Conceptual Survey of Electricity and Magnetism test in a calculus-based introductory physics course. Students who collaborated with a peer showed significantly larger normalized gain on individual testing than those who did not collaborate. We did not find statistically significant differences between the performance of students who were given an opportunity to formulate their own response before the peer discussions, compared to those who were not. Peer collaboration also shows evidence for the co-construction of knowledge. Discussions with individual students show that students themselves value peer interaction. We discuss the effect of pairing students with different individual achievements.
TL;DR: This paper endeavors to explain, in a fashion comprehensible to the nonexpert, the RSA encryption protocol; the various quantum computer manipulations constituting the Shor algorithm; how theShor algorithm performs the factoring; and the precise sense in which a quantum computer employing Shor’s algorithm can be said to accomplish the factored of very large numbers with less computational effort than a classical computer.
Abstract: The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (conventional) computers. In 1994 Peter Shor showed that for sufficiently large N, a quantum computer could perform the factoring with much less computational effort. This paper endeavors to explain, in a fashion comprehensible to the nonexpert, the RSA encryption protocol; the various quantum computer manipulations constituting the Shor algorithm; how the Shor algorithm performs the factoring; and the precise sense in which a quantum computer employing Shor’s algorithm can be said to accomplish the factoring of very large numbers with less computational effort than a classical computer. It is made apparent that factoring N generally requires many successive runs of the algorithm. Our analysis reveals that the probability of achieving a successful factorization on a single run is about twice as large as commonly quoted in the literature.
TL;DR: In this paper, the authors present the results of a case study of an experienced physics instructor as he attempted to change his instructional practices, and identify four factors that limited his ability to change: an implicit instructional model, incomplete knowledge of instructional strategies, overly optimistic initial planning, and a desire to work within perceived external constraints.
Abstract: Physics education researchers have compiled substantial evidence that student course outcomes can be improved if physics instructors incorporate research-based instructional strategies into their teaching. Some instructors find this evidence convincing and attempt to change their instruction. Some of these instructors are successful and some are not. This paper presents the results of a case study of an experienced physics instructor as he attempted to change his instructional practices. Although the instructor appeared to have the prerequisites for successful change, he still encountered difficulties. Four factors were identified that limited his ability to change: an implicit instructional model, incomplete knowledge of instructional strategies, overly optimistic initial planning, and a desire to work within perceived external constraints. Contrary to common models of instructional change, the instructor did not attempt to learn many details about available techniques and engaged in a significant amount...
TL;DR: The Collapse of the "Classical" World View is presented as a guide to a Coherent Framework for All Physical Processes for the Reconstruction of the Universe in the 21st Century.
Abstract: Preface xi Acknowledgments xvii Chapter One: The Collapse of the \"Classical\" World View 1 Chapter Two: The Polarization of Light 25 Chapter Three: Quanta, Chance Events, and Indeterminism 43 Chapter Four: The Superposition Principle and the Conceptual Structure of the Theory 79 Chapter Five: Visualization and Scientific Progress 111 Chapter Six: The Interpretation of the Theory 120 Chapter Seven: The Bohr-Einstein Dialogue 149 Chapter Eight: A Bolt from the Blue: The Einstein-Podolski-Rosen Argument 165 Chapter Nine: Hidden Variables 195 Chapter Ten: Bell's Inequality and Nonlocality 226 Chapter Eleven: Nonlocality and Superluminal Signals 261 Chapter Twelve: Quantum Cryptography 292 Chapter Thirteen: Quantum Computers 313 Chapter Fourteen: Systems of Identical Particles 331 Chapter Fifteen: From Microscopic to Macroscopic 344 Chapter Sixteen: In Search of a Coherent Framework for All Physical Processes 377 Chapter Seventeen: Spontaneous Localization, Properties, and Perceptions 416 Chapter Eighteen: Macrorealism and Noninvasive Measurements 437 Chapter Nineteen: Conclusions 448 Notes 455 Bibliography 473 Index 477
TL;DR: In this paper, a simple formulation of the basic equation of general relativity in terms of the motion of freely falling test particles is given, and the consequences of this formulation are sketched.
Abstract: This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein’s equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of the consequences of this formulation and explain how it is equivalent to the usual one in terms of tensors. Finally, we include an annotated bibliography of books, articles, and websites suitable for the student of relativity.
TL;DR: In this paper, the wave function of a free electron in a strong laser field is used to obtain nonperturbative results for the cross-section for laser-assisted scattering and the laser assisted photoelectric effect.
Abstract: When electrons, atoms, and molecules are in a strong laser field, the wave function of the continuum electron plays an important role. Nonperturbative results for the cross-section for laser-assisted scattering and the laser-assisted photoelectric effect are obtained using the Volkov wave function of a free electron in a laser field. Also derived is the rate for strong-field electron detachment from negative ions.
TL;DR: In this article, a simple derivation of the Schwarzschild solution in general relativity based on an approach by Weyl, but generalized to include Birkhoff's theorem was provided.
Abstract: We provide a simple derivation of the Schwarzschild solution in general relativity based on an approach by Weyl, but generalized to include Birkhoff’s theorem. This theorem states that the Schwarzschild mass must be constant in time. Our procedure is illustrated by a parallel derivation of the Coulomb field and the constancy of the electric charge in electrodynamics. We also explain the basis of Birkhoff’s theorem and note that even the original Weyl approach can be used to illuminate the special role played by the Schwarzschild coordinates.
TL;DR: For example, this paper pointed out that learning is inherently more compressive than most physical processes, and that unless we are willing to apply the same rigorous standards of scholarship to is related to learning and teaching that we regularly apply more traditional research, the present situation in phy education is unlikely to change.
Abstract: of e a ch of ning During the World Year of Physics, much effort is bein made to celebrate the unprecedented advances in our u standing of the physical world made during the past cent However, we have not yet seen comparable advances in understanding of student learning of our discipline. One p sible explanation is that learning is inherently more comp than most physical processes. Although this explanatio plausible, we have not made similar systematic efforts understand student learning. The enormous effort expen by many physics instructors over the past century was harnessed in a way that made cumulative progress likely Lillian McDermott has observed, ‘‘Unless we are willing t apply the same rigorous standards of scholarship to is related to learning and teaching that we regularly apply more traditional research, the present situation in phy education is unlikely to change.’’ 1